聊聊神经网络模型预训练生成超参数实现-526互联

概述

在上一篇博客中，已经阐述了预训练过程中，神经网络中超参数的计算逻辑，本文，从程序实现的角度，将数学计算转换为程序代码，最终生成超参数文件；并将替换聊聊神经网络模型示例程序——数字的推理预测中已训练好的超参数文件，推理预测数字，最终比对下两者的精确度。

神经网络层实现

首先，根据神经网络各个层的计算逻辑用程序实现相关的计算，主要是：前向传播计算、反向传播计算、损失计算、精确度计算等，并提供保存超参数到文件中。

# coding: utf-8
import sys, os
sys.path.append(os.pardir)  # 为了导入父目录的文件而进行的设定
from DeepLearn_Base.common.functions import *
from DeepLearn_Base.common.gradient import numerical_gradient
import pickle

# 三层神经网络处理类(两层隐藏层+1层输出层)
class ThreeLayerNet:

    # input_size:输入层神经元数量，灰度图像的三维表示: 1 * 28 * 28 = 784
    # output_size: 输出层神经元数量，10，表示10个数字
    # hidden_size：第一层隐藏层神经元数量，50
    # second_hidden_size：第二层隐藏层神经元数量，100
    # weight_init_std：权重初始化
    def __init__(self, input_size, hidden_size, output_size, second_hidden_size, weight_init_std=0.01):
        # 初始化权重
        self.params = {}
        self.params['W1'] = weight_init_std * np.random.randn(input_size, hidden_size)
        self.params['b1'] = np.zeros(hidden_size)
        self.params['W2'] = weight_init_std * np.random.randn(hidden_size, second_hidden_size)
        self.params['b2'] = np.zeros(second_hidden_size)
        self.params['W3'] = weight_init_std * np.random.randn(second_hidden_size, output_size)
        self.params['b3'] = np.zeros(output_size)

    # 执行预测
    def predict(self, x):
        W1, W2, W3 = self.params['W1'], self.params['W2'], self.params['W3']
        b1, b2, b3 = self.params['b1'], self.params['b2'], self.params['b3']
    
        # 隐藏层第一层
        a1 = np.dot(x, W1) + b1
        z1 = sigmoid(a1)

        # 隐藏层第二层
        a2 = np.dot(z1, W2) + b2
        z2 = sigmoid(a2)
        
        # 输出层
        a3 = np.dot(z2, W3) + b3
        y = softmax(a3)
        
        return y
        
    # x:输入数据, t:监督数据
    def loss(self, x, t):
        y = self.predict(x)
        
        return cross_entropy_error(y, t)
    
    # 精确度计算
    def accuracy(self, x, t):
        y = self.predict(x)
        y = np.argmax(y, axis=1)
        t = np.argmax(t, axis=1)
        
        accuracy = np.sum(y == t) / float(x.shape[0])
        return accuracy
        
    # 梯度计算
    def gradient(self, x, t):
        W1, W2, W3 = self.params['W1'], self.params['W2'], self.params['W3']
        b1, b2, b3 = self.params['b1'], self.params['b2'], self.params['b3']
        grads = {}
        
        batch_num = x.shape[0]
        
        # forward
        # 隐藏层第一层
        a1 = np.dot(x, W1) + b1
        z1 = sigmoid(a1)

        # 隐藏层第二层
        a2 = np.dot(z1, W2) + b2
        z2 = sigmoid(a2)
        
        # 输出层
        a3 = np.dot(z2, W3) + b3
        y = softmax(a3)
        
        # backward
        # 两层隐藏层计算梯度
        # 输出层梯度: Loss与输出的导数，分类场景下，等于预测值-真实值
        # 权重梯度: 隐藏层输出的转置 * 损失函数梯度
        dy = (y - t) / batch_num
        grads['W3'] = np.dot(z2.T, dy)
        grads['b3'] = np.sum(dy, axis=0)
        
        # 反向传播到隐藏层
        # 隐藏层梯度:Loss与输出的导数 * 输出层权重的转置
        da2 = np.dot(dy, W3.T)
        dz2 = sigmoid_grad(a2) * da2
        grads['W2'] = np.dot(z1.T, dz2)
        grads['b2'] = np.sum(dz2, axis=0)

        da1 = np.dot(da2, W2.T)
        dz1 = sigmoid_grad(a1) * da1
        grads['W1'] = np.dot(x.T, dz1)
        grads['b1'] = np.sum(dz1, axis=0)

        return grads
    
    # 保存参数到文件
    def save_params(self, file_name="params.pkl"):
        params = {}
        for key, val in self.params.items():
            params[key] = val
        with open(file_name, 'wb') as f:
            pickle.dump(params, f)

预训练实现

读取MNIST训练数据集，总共有60000个。每次从60000个训练数据中随机取出100个数据 (图像数据和正确解标签数据)。然后，对这个包含100笔数据的批数据求梯度，使用随机梯度下降法(SGD)更新参数。这里，梯度法的更新次数(循环的次数)为10000。每更新一次，都对训练数据计算损失函数的值，并把该值添加到数组中。

# coding: utf-8
import sys, os
sys.path.append(os.pardir)  # 为了导入父目录的文件而进行的设定
import numpy as np
import matplotlib.pyplot as plt
from DeepLearn_Base.dataset.mnist import load_mnist
from three_layer_net import ThreeLayerNet

# 读入数据
# x_train.sharp 60000 * 784
# t_train.sharp 60000 * 10
(x_train, t_train), (x_test, t_test) = load_mnist(normalize=True, one_hot_label=True)

network = ThreeLayerNet(input_size=784, hidden_size=50, second_hidden_size=100, output_size=10)

iters_num = 10000  # 适当设定循环的次数
# 训练集大小 60000
train_size = x_train.shape[0]
batch_size = 100
learning_rate = 0.1

train_loss_list = []
train_acc_list = []
test_acc_list = []

# 每批次迭代数量：600
iter_per_epoch = max(train_size / batch_size, 1)

for i in range(iters_num):
    # 从训练集中选取100个为一批次进行训练
    batch_mask = np.random.choice(train_size, batch_size)
    x_batch = x_train[batch_mask]
    t_batch = t_train[batch_mask]
    
    # 更新超参数梯度
    grad = network.gradient(x_batch, t_batch)
    
    # 更新超参数W,b
    for key in ('W1', 'b1', 'W2', 'b2', 'W3', 'b3'):
        network.params[key] -= learning_rate * grad[key]
    
    loss = network.loss(x_batch, t_batch)
    train_loss_list.append(loss)
    
    if i % iter_per_epoch == 0:
        train_acc = network.accuracy(x_train, t_train)
        test_acc = network.accuracy(x_test, t_test)
        train_acc_list.append(train_acc)
        test_acc_list.append(test_acc)
        print("train acc, test acc | " + str(train_acc) + ", " + str(test_acc))

# 绘制图形
markers = {'train': 'o', 'test': 's'}
x = np.arange(len(train_acc_list))
plt.plot(x, train_acc_list, label='train acc')
plt.plot(x, test_acc_list, label='test acc', linestyle='--')
plt.xlabel("epochs")
plt.ylabel("accuracy")
plt.ylim(0, 1.0)
plt.legend(loc='lower right')
plt.show()

# 输出到文件保存参宿后
network.save_params("E:\\workcode\\code\\DeepLearn_Base\\ch04\\myparams.pkl")

用图像来表示这个损失函数的值的推移，如图所示；并保存最终的超参数到pkl文件。